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Collaborative Research:
Adaptation & Implementation of
Activity & Web-Based Materials
Into Post-Calculus Introductory
Probability and Statistics Courses
Tracy Goodson-Espy
M. Leigh Lunsford
Ginger Holmes Rowell
NSF DUE-0126716
A Collaborative Approach
A&I Materials into Post Calculus Prob/Stat Courses
Athens State Univ.
Middle Tenn. St. Univ.
M. Leigh Lunsford
Ginger Holmes Rowell
Univ. of Alabama, Huntsville
Tracy Goodson-Espy
Provide Objective Independent Assessment of A&I
NSF DUE-0126716
Project* Objectives
• To improve post-calculus students
learning of probability & statistics.
• To provide students with better
preparation for their future careers in
mathematics & statistics, mathematics
education, and computer science.
*This project is partially supported by the National Science Foundation. The
project started in June, 2002 and continues through August, 2004.
NSF DUE-0126716
The Materials for A&I
• “A Data-Oriented, Active Learning, PostCalculus Introduction to Statistical
Concepts, Methods, and Theory (SCMT)”
• A. Rossman, B. Chance, K. Ballman
• NSF DUE-9950476
• “Virtual Laboratories in Probability and
Statistics (VLPS)”
• K. Siegrist
• NSF DUE-9652870
NSF DUE-0126716
Statistical Concepts, Methods, and Theory
(SCMT): A Small Sample of Materials
Activity
Context
Concepts
Description
Friendly
Observers
Randomization,
simulation, p-value
Uses cards (23 per student) and Minitab to
simulate a randomization test to estimate pvalue from a 2x2 table for a psychology study.
Equal
Likeliness
Random
Babies
Sample space, long-run
relative frequency,
random variable,
expected value,
simulation
Uses index cards (4 per student) and Minitab to
simulate the matching problem and develops
probability calculations with equally likely
outcomes.
Fishers
Exact Test
Friendly
Observers
Counting rules,
hypergeometric
probabilities
Exact probabilities for simulation in
Randomization Test
General vs.
Specific
The Birthday
Problem
Applications of counting
techniques, complement
rule
Does calculations for the birthday problem
(using a spreadsheet) contrasting any birthday
vs. a specific birthday
Prob. Rules
100 top films,
2000 Michigan
primary
Variety of basic
probability rules
Discovery approach through two-way tables and
some Venn diagrams. HW is very interesting
Randomization Test
NSF DUE-0126716
Virtual Laboratories in Probability &
Statistics: An Example
Games of Chance
Contents
1. Poker
2. Poker Dice and Chuck-a-Luck
3. Craps
4. Introduction
5. Roulette
6. The Monty Hall Problem
7. Lotteries
8. Notes
Applets
•
Poker Experiment
•
Poker Dice Experiment
•
Chuck-a-Luck Experiment
•
Craps Experiment
•
Roulette Experiment
•
Monty Hall Game
•
Poker Experiment Applet
Monty Hall Experiment
NSF DUE-0126716
The A&I Cycle
Receive Training
on New Materials
Develop Best
Practices for Use
of Materials Co-jointly
Materials
VLPS
Use Materials
in Courses
SCMT
Provide Feedback to
Material Developers
Evaluate A&I
Refine Adaptation
Use Independent
Assessment Results
to Improve A&I
NSF DUE-0126716
Courses for A&I
ASU:
•Applied Statistics & Probability I (3 hrs)
Clientele: CS, MA, Math. Ed. Majors
Prereq: Calculus II
MTSU:
•Probability & Statistics (3 hrs)
•Data Analysis (1 hr)
Clientele: CS, Math. Ed. Majors
Prereq: Calculus I
NSF DUE-0126716
Topics in ASU’s Course
•Topics Included:
•Random Experiments, Sample Spaces, Random Samples
•Basic Descriptive Statistics (Mean, Var., Std. Dev., Sample Mean and Var.)
•Probability Theory:
Laws of Probability, Conditional Probability, Independence, Law of Total
Probability, Bayes’ Theorem
•Discrete and Continuous Random Variables
Uniform (discrete & continuous), Binomial, Hypergeometric, Geometric,
Normal, pdf vs. cdf.
•Expected Value
•Central Limit Theorem
•Confidence Intervals for Means & Proportions
•Basic Concepts in Hypothesis Testing
•Topics Not Included:
•Multivariate Distributions
•Moment Generating Functions
NSF DUE-0126716
An Example
Friendly Observers Experiment*:
•Researchers investigated a conjecture that having an observer with a vested interest
would decrease subjects’ performance on a skill-based task.
•Subjects given time to practice task.
•Subjects randomly assigned to one of two groups:
•Group (A) was told that the participant and observer would each win $3 if the
participant beat a certain threshold time.
•Group (B) was told only that the participant would win $3 if the threshold were
beaten.
•Threshold chosen to be a time that participant beat in 30% of their practice
turns.
A: observer shares prize B: no sharing of prize
Total
Beat threshold
3
8
11
Do not beat threshold
9
4
13
Total
12
12
24
*Journal of Personality and Social Psychology (Butler and Baumeister, 1998)
NSF DUE-0126716
An Example
Week 1: Activity with the Friendly Observers Experiment
•Concepts: Randomness, random variable, empirical probability
distribution, p-value. (Hypothesis testing)
•Uses a tactile simulation (in-class) and Minitab (assignment) to
determine the empirical probability distribution for the random
variable X (the number of winners assigned to group A by chance).
•Students start writing a report detailing their simulation results and
their empirical estimate of the p-value.
Week 3: Follow-up activity includes Friendly Observers Exper.
•Concepts: Hypergeometic probabilities and the hypergeometric
distribution.
•Students apply theory to Friendly Observers Experiment above
to compute the probability distribution of X and the
actual p-value of the experiment.
•Uses the Ball and Urn Applet from the Virtual Labs.
•Students finish report.
NSF DUE-0126716
Project Goals and Outcomes
•
The development of post-calculus probability and statistics courses that
produce well-educated students.
•
The integration of technology and group-based activity work into the
courses for the purpose of enhancing student learning.
•
The enhancement of student communication skills through oral and written
reports and presentations.
•
The improvement and implementation of non-traditional assessment
techniques for evaluating students.
•
A contribution to the mathematics community discussion/research
concerning what topics/materials/methods should be included in reformoriented probability and statistics courses to improve overall student
understanding of the subject.
NSF DUE-0126716
Assessment of A&I of Materials
• Will Use an Action Research Model*
– What is the problem? I.e., what is not
working in the classroom?
– What technique can be used to address the
learning problem?
– What type of evidence can be gathered to
show whether the implementation is
effective?
– What should be done next, based on what
was learned?
*1999 - R. delMas, J. Garfield, B. Chance
NSF DUE-0126716
Teaching Experiment Cycle
Teaching Hypotheses;
Curricular & Instructional
Choices
Class
Implementation
& Feedback
Instructors’ Reflections and
Curricular Modifications
NSF DUE-0126716
Preliminary Survey
•
Students in the project classes were given mid-term
and final Class Activities Surveys. These surveys
consisted of three parts:
•
•
•
•
Section One asked a series of questions concerning student’s
beliefs concerning his/her understanding of specific mathematics
concepts covered in the course such as sample space, conditional
probability, independence of events, probability laws, etc. The
student was asked to rate their understanding on a 1-5 scale(L-H).
Section Two included a series of questions that asked students to
rate the functioning of the class in terms of class dynamics, group
dynamics, instructional strategies used, amount of technology
used, and the effectiveness of the technology for conveying ideas.
Section Three included open-ended questions that solicited
student opinions.
This survey was also given to pre-project classes in Spring 2002.
NSF DUE-0126716
Further Data Acquisition
• During the spring term 2003, each project
class will be observed repeatedly by the
project evaluator.
• Individual videotaped teaching interviews
will be conducted with selected students
from each class and case studies will be
developed from these interviews and the
written artifacts of student work including,
tests, homework, and reports.
NSF DUE-0126716
Dissemination
• Presentations at Professional Conferences
• In-Service Training for High School Statistics
Teachers (Spring 2004)
• Summer Workshop for College Faculty
(Summer 2004)
• Papers in Mathematics Education Journals
• Project Website:
http://www.athens.edu/NSF_Prob_Stat/
NSF DUE-0126716